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Faster methods for contracting infinite two-dimensional tensor networks

(2018) PHYSICAL REVIEW B. 98(23).
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Abstract
We revisit the corner transfer matrix renormalization group (CTMRG) method of Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and demonstrate that its performance can be substantially improved by determining the tensors using an eigenvalue solver as opposed to the power method used in CTMRG. We also generalize the variational uniform matrix product state (VUMPS) ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer matrices and discuss similarities with the corner methods. These two new algorithms will be crucial to improving the performance of variational infinite projected entangled pair state (PEPS) methods.
Keywords
MATRIX RENORMALIZATION-GROUP, MANY-BODY THEORIES, DENSITY-MATRIX, EXPONENTIAL OPERATORS, THERMODYNAMICS, ALGORITHMS, MODELS, CHAIN

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Please use this url to cite or link to this publication:

Chicago
Fishman, MT, Laurens Vanderstraeten, V Zauner-Stauber, Jutho Haegeman, and Frank Verstraete. 2018. “Faster Methods for Contracting Infinite Two-dimensional Tensor Networks.” Physical Review B 98 (23).
APA
Fishman, M., Vanderstraeten, L., Zauner-Stauber, V., Haegeman, J., & Verstraete, F. (2018). Faster methods for contracting infinite two-dimensional tensor networks. PHYSICAL REVIEW B, 98(23).
Vancouver
1.
Fishman M, Vanderstraeten L, Zauner-Stauber V, Haegeman J, Verstraete F. Faster methods for contracting infinite two-dimensional tensor networks. PHYSICAL REVIEW B. 2018;98(23).
MLA
Fishman, MT et al. “Faster Methods for Contracting Infinite Two-dimensional Tensor Networks.” PHYSICAL REVIEW B 98.23 (2018): n. pag. Print.
@article{8588534,
  abstract     = {We revisit the corner transfer matrix renormalization group (CTMRG) method of Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and demonstrate that its performance can be substantially improved by determining the tensors using an eigenvalue solver as opposed to the power method used in CTMRG. We also generalize the variational uniform matrix product state (VUMPS) ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer matrices and discuss similarities with the corner methods. These two new algorithms will be crucial to improving the performance of variational infinite projected entangled pair state (PEPS) methods.},
  articleno    = {235148},
  author       = {Fishman, MT and Vanderstraeten, Laurens and Zauner-Stauber, V and Haegeman, Jutho and Verstraete, Frank},
  issn         = {2469-9950},
  journal      = {PHYSICAL REVIEW B},
  keywords     = {MATRIX RENORMALIZATION-GROUP,MANY-BODY THEORIES,DENSITY-MATRIX,EXPONENTIAL OPERATORS,THERMODYNAMICS,ALGORITHMS,MODELS,CHAIN},
  language     = {eng},
  number       = {23},
  pages        = {17},
  title        = {Faster methods for contracting infinite two-dimensional tensor networks},
  url          = {http://dx.doi.org/10.1103/PhysRevB.98.235148},
  volume       = {98},
  year         = {2018},
}

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